Here’s a conversation between two mathematicians:
First: “I have three children. The product of their ages is 36. If you sum their ages, it is exactly same as my neighbor’s door number on my left. What are their ages?”
Second: Takes a look at the door number and verifies it. “Well, that data is not enough.”
First: “One more clue. My youngest is the youngest”
Immediately the second mathematician finds out their ages. Can you?
How many possible factors are there for 36 using three numbers?
Of these, only #1 has unique set of ages, i.e., every age is different. This is necessary to validate the second clue of “My youngest is the youngest”.
So, the answer is 2, 3 and 6.
That bit about the neighbor’s door is just a diversion.
Alas, not a great puzzle -- because while "1" isn't allowed when coming up with prime factors, it is a perfectly valid age. So there's nothing in the puzzle to prevent the answer from being
1, 2, 18
1, 3, 12
1, 4, 9
1, 6, 6
...unless of course I'm too low on sleep to understand things correctly :)
Right on, I overlooked that part! Thanks for the catch.
no diversion, there is a bit more logic behind that puzzle.
first you missed one more combination -> 36 = 1 x 1 x 36 is possible as well ;-)
but the trick is the door number. in most cases if you add the ages the result (and door number) is a unique number, with the exception of 13:
13=1+6+6 and 13=2+2+9
so now you should see why the hint was necessary. only in this case the look-up of the door number was insufficient.
the hint shows that there is only "one" smallest age, thus 1,6,6 is the correct solution.
Greetings and a happy New Year from germany :)
Thanks Gerald, you are right.
I am an old puzzle fan, I heard about this puzzle 25 years ago, with another story around it. There it was a selling agent who had to solve the puzzle in order to sell his product.